Question

Radioactive isotopes of iodine are often used in medical settings to improve the images from x-rays and CT scans. A patient is given a 1 fluid ounce solution containing 120 micrograms of iodine, which is 10% by mass radioactive iodine-123, and the remainder is stable iodine-127. A. Determine the molar concentration of both iodine-123 and iodine-127 in the solution. B. If iodine-123 is absorbed with 80% efficiency into the bloodstream, how many atoms of iodine-123 will make it into the patient's blood?

Answer 1

Solution: Total mass of iodine = 120 micrograms

Mass of iodine-123 = 10% of 120 micrograms = 120 x 10/100 = 12 micrograms = 12 x 10-6 g, then

Mass of iodine-127 = 120 -12 =108 micrograms =108 x 10-6 g

Molar concentration (mol/L) = (mass (g) / molar mass x Volume in L)

Molar concentration of iodine-127 = 108 x 10^-6 / 127x1 =0.85 x 10^-6 = 8.5 x 10^-7 M

Molar concentration of iodine-123 = 12 x 10^-6 / 123x1 =0.097 x 10^-6 = 0.97 x 10^-7 M

Total number of atoms in iodine -123

Since 6.023 x 10²³ atoms are present in 1 mole of iodine-123, then

0.97 x 10^-7 mole contains = 0.7 x 10^-7 x 6.023 x 10²³ = 4.216 x 10¹⁶ atoms

Since iodine-123 is only 80% absorbed, hence total absorbed atoms of iodine-123 = 4.216 x 10¹⁶ atoms x 80/100

= 3.37 x 10¹⁶ atoms